| Reference : Dirichlet-Ford domains and double Dirichlet domains |
| Scientific journals : Article | |||
| Physical, chemical, mathematical & earth Sciences : Mathematics | |||
| http://hdl.handle.net/10993/45742 | |||
| Dirichlet-Ford domains and double Dirichlet domains | |
| English | |
Jespers, E.  [> >] | |
| Juriaans, S. O. [> >] | |
| Kiefer, Ann [University of Luxembourg > Faculty of Humanities, Education and Social Sciences (FHSE) > LUCET] | |
| de A. e Silva, A. [> >] | |
| Souza Filho, A. C. [> >] | |
| 2016 | |
| Bulletin of the Belgian Mathematical Society Simon Stevin | |
| 23 | |
| 3 | |
| 465--479 | |
| Yes (verified by ORBilu) | |
| 1370-1444 | |
| 2034-1970 | |
| [en] Hyperbolic Space ; Kleinian Groups ; Fundamental Domains | |
| [en] We continue investigations started by Lakeland on Fuchsian and Kleinian groups which
have a Dirichlet fundamental domain that also is a Ford domain in the upper half-space model of hyperbolic 2- and 3-space, or which have a Dirichlet domain with multiple centers. Such domains are called DF-domains and Double Dirichlet domains respectively. Making use of earlier obtained concrete formulas for the bisectors defining the Dirichlet domain of center i ∈ H 2 or center j ∈ H 3 , we obtain a simple condition on the matrix entries of the side- pairing transformations of the fundamental domain of a Fuchsian or Kleinian group to be a DF-domain. Using the same methods, we also complement a result of Lakeland stating that a cofinite Fuchsian group has a DF domain (or a Dirichlet domain with multiple centers) if and only if it is an index 2 subgroup of the discrete group G of reflections in a hyperbolic polygon. | |
| http://hdl.handle.net/10993/45742 |
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